The spinothalamic tract does not pass near C. The pain pathway on the right has the 1st neuron in the right dorsal root ganglion which synapses with the 2nd neuron in the dorsal horn on the right (between B and D). The 2nd neuron's axons pass through the anterior commissure to the opposite side at the same level and ascends in the spinothalamic tract on the contralateral (left) side which is labeled E. C is the left lateral corticospinal tract which contains descending fibers of the upper motor neuron that innervates the left side.
Basically take the image from the link you posted and look at the mirror image and it'll show the pathway in the question stem.
So the answer is E because it is the only labeled component in the pain pathway from the right side.
The UES is a sphincter and all sphincters in the GI are constitutively contracted and relaxes when stimulated to let food pass through which eliminates C and E since those show just a contraction and contracting the UES would inhibit swallowing. A wouldn't make sense because it shows a relaxation without any subsequent contraction. When you swallow your throat doesn't just open up and stay that way because then you wouldn't be able to breathe since the the epiglottis needs to cover the larynx. Also a sphincter's baseline state is contracted. So that leaves B and D which both show a relaxation followed by a contraction and then return to baseline pressure. The relaxation lets the food through to the esophagus and the contraction is the peristalsis that pushes the bolus of food downwards. The difference between the two answer choices is time scale. Here you can just do a voluntary swallow and figure out that it doesn't take you 10+ seconds to swallow something. So that rules out B and leaves D.
